Poisson involutions, spin Calogero-Moser systems associated with symmetric Lie subalgebras and the symmetric space spin Ruijsenaars-Schneider models

Details Poisson involutions, spin Calogero-Moser systems associated with symmetric Lie subalgebras and the symmetric space spin Ruijsenaars-Schneider models Poisson involutions, spin Calogero-Moser systems associated with symmetric Lie subalgebras and the symmetric space spin Ruijsenaars-Schneider models

2005-06-10

arxiv.org/abs/math-ph/0506025v1

Comm. Math. Phys. 265 (2006), no. 2, 333-372

Physics

Mathematical Physics

48 pages

Scientific paper

10.1007/s00220-006-0012-6

We develop a general scheme to construct integrable systems starting from realizations in symmetric coboundary dynamical Lie algebroids and symmetric coboundary Poisson groupoids. The method is based on the successive use of Dirac reduction and Poisson reduction. Then we show that certain spin Calogero-Moser systems associated with symmetric Lie subalgebras can be studied in this fashion. We also consider some spin-generalized Ruisjenaars- Schneider equations which correspond to the $N$-soliton solutions of $A^{(1)}_n$ affine Toda field theory. In this case, we show how the equations are obtained from the Dirac reduction of some Hamiltonian system on a symmetric coboundary dynamical Poisson groupoid.

Affiliated with

Also associated with

No associations

Rating

Poisson involutions, spin Calogero-Moser systems associated with symmetric Lie subalgebras and the symmetric space spin Ruijsenaars-Schneider models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Poisson involutions, spin Calogero-Moser systems associated with symmetric Lie subalgebras and the symmetric space spin Ruijsenaars-Schneider models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Poisson involutions, spin Calogero-Moser systems associated with symmetric Lie subalgebras and the symmetric space spin Ruijsenaars-Schneider models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-730235